German Letters Patent 42 34 151 discloses that the heat from the exhaust gases of high temperature fuel cells exploitable via heat exchangers and via normal flow heaters. German Letters Patent 40 32 993 discloses that the anode exhaust gas of a fuel module, which can, among other things, also be a low-temperature fuel cell module, can be utilized for combustion. It is provided in the embodiment with high-temperature fuel cells contained in this Prior Art that the hot exhaust gases from the high-temperature fuel cells are utilized for pre-heating the as yet unheated fuels that are rich in H.sub.2. Up to now, however, no method and no system for the implementation of a method has been disclosed wherein the enthalpy contained in the exhaust gases of low-temperature fuel cells is exploited for increasing the overall efficiency of an energy supply system.